but maybe it would have a greater effect in US politics if Irish-American organizations were made aware of it and established direct ties with German diplomats you could have perhaps an anti-war candidate challenging Wilson at the 1916 convention.
It would certainly have some effect, but it could easily be negative for Germany, depending on the butterflies. And unless Germany changes policy, either Wilson or Hughes likely enters the war. Unless the root causes are addressed, it doesn't change anything. It is like a man 150 pounds over weight who eats 4000 calories per day and has severe heart disease trying to get healthy by exercising 2 minutes per day.
Germany had WW1 largely won, and it had the ability to keep the USA out of the war, it just took the wrong path. And the blame lies 100% with the 20 most senior government officials of Germany. Despite Conrads screwups, and the blockade, and Italy entering the war, and Romania entering the war, and Verdun not working out, Germany had it won, if it just understood not to bring the USA in the war.
Unrestricted Submarine warfare was just marginally more efficient than following cruiser rules on tonnage per day per submarine. It took 10-12 hours on average for the RN to respond to a distress call. All the data to understand what was happening was in the German Navy records. Germany just chose the "wonder weapon" of unrestricted submarine warfare over continuing a policy that was working OK. The main variable for tonnage sunk per day was number of subs on station per day.
The Zimmerman telegram was ASB stupid. I have seen plenty of TL moved to the ASB section for more likely POD's and butterflies.
And the diplomacy leading up to the war was horrible. If the Kaiser set out each day to offend foreign nations, he could not have done much better. And after June 1914, it is horrible. No coordination of War Plans with A-H. Not building the case for war by A-H. They had captured the killer, Serbian intelligence was involved, yet the CP don't sell the case. If half the American public understands that Serbia's intelligence was involved in assassination of foreign leaders, the USA does not enter the war. Italy is not kept informed, so it has a good excuse to not join the war for the CP. Neutrality is about the best that can be hopped for by the CP, but using July 1914 to sell to the Italians that Serbia is the dangerous aggressor. The peace efforts are horribly bungled. Something as simple as the Kaiser meeting in Switzerland with the Pope with something sounding like a reasonable peace offer would have a huge impact. Or just a reasonable sounding peace offer. Sure Wilson was calling for ethnic minorities to get freedom. Counter offer that German is ok with that, provide everyone gets them including the Irish, SE France, etc. A good diplomat can write a peace offer that sounds great in headlines, but when the negotiations begin, has plenty of wiggle room to escape.
As good as the German Army was in WW1, its diplomacy was that bad.